In this paper, we extend the notion of Cauchy-Schwarz divergence to point processes and establish that the Cauchy-Schwarz divergence between the probability densities of two Poisson point processes is half the squared L2-distance between their intensity functions. Extension of this result to mixtures of Poisson point processes and, in the case where the intensity functions are Gaussian mixtures, closed form expressions for the Cauchy-Schwarz divergence are presented. Our result also implies that the Bhattacharyya distance between the probability distributions of two Poisson point processes is equal to the square of the Hellinger distance between their intensity measures. We illustrate the result via a sensor management application where the system states are modeled as point processes.

This paper proposes a systematic approach for the design of a general class of analog infinite-impulse-response (IIR) filters, which includes all well-known classical analog filters as a special case. All specifications including the conventional ones and also filter flatness degrees are explicitly incorporated into design process. Several numerical examples are presented to demonstrate the efficiency and flexibility of the proposed method.

For a transfer function/filter F(ejω) of order n, Kalman-Yakubovich-Popov (KYP) lemma characterizes the intractable semi-infinite programming (SIP) condition F(e-jω)1 Θ [F(ejω)1]T≥ 0 ∀ ω in frequency domain by a tractable semi-definite programming (SDP) in state-space domain. Some recent results generalize this lemma to SDP for SIP of frequency selectivity (FS-SIP). All these SDP characterizations are given at the expense of the introduced Lyapunov matrix variable of dimension n × n, making them impractical for high order problem. Moreover, the existing SDP characterizations for FS-SIP do not allow to formulate synthesis/design problems as SDPs. In this paper, we propose a completely new SDP characterization of general FS-SIP, which is of moderate size and is free from Lyapunov variables. Extensive examples are provided to validate the effectiveness of our result.